WASHINGTON — Restaurant chains like McDonald’s want to keep their lucrative tax credit for hiring veterans. Altria, the tobacco company, wants to cut the corporate tax rate. And Sapphire Energy, a small alternative energy company, is determined to protect a tax incentive it believes could turn algae into a popular motor fuel.

As Congress prepares to debate a rewrite of the nation’s tax code, this diverse set of businesses has at least one strategy in common: They have retained firms that employ lobbyists who are former aides to Max Baucus, chairman of the Senate Finance Committee, which will have a crucial role in shaping any legislation.

No other lawmaker on Capitol Hill has such a sizable constellation of former aides working as tax lobbyists, representing blue-chip clients that include telecommunications businesses, oil companies, retailers, and financial firms, according to an analysis by Legi­Storm, an online database that tracks congressional staff members and lobbying.

At least 28 aides who worked for the Montana Democrat since he became the committee chairman in 2001 have lobbied on tax issues during the Obama administration — more than any other current member of Congress, according to the analysis of lobbying filings performed for The New York Times.

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‘‘K Street is literally littered with former Baucus staffers,’’ said Jade West, an executive at a wholesalers’ trade association that relies on a former finance panel aide, Mary Burke Baker. ‘‘It opens doors that allow you to make the case.’’

Like Baker, many of those lobbyists have saved their clients millions — in some cases, billions — of dollars after Baucus backed their requests to extend certain corporate tax perks, provisions that were adopted as part of the ‘‘fiscal cliff’’ legislation in January.

Baucus aides who later became lobbyists helped financial firms save $11.2 billion in tax deferments and helped secure a $222 million tax benefit that is shared with the liquor industry.

Sean Neary, a spokesman for Baucus, said the senator had regularly rejected requests from those lobbyists for provisions benefiting their clients, like an appeal from one former aide, Pat Bousliman, now working as a wind industry lobbyist, to extend an alternative energy loan guarantee program that expired in 2011.

Baucus’s decisions are based on the merits of the policies, Neary said, not on who is advocating for them. ‘‘The fact is, oftentimes good policy can indirectly benefit someone,’’ he said. ‘‘That doesn’t mean it shouldn’t be done.’’

Baucus, who has spent nearly his entire professional career in Congress, declined a request for an interview. But Neary said that every action the senator takes is motivated by his commitment to voters.

Several veteran Capitol Hill aides said it was naive to suggest that former aides could extract special favors from their one-time bosses unless what they were pushing for had broad support. But the former aides still bring an advantage to the corporations that hire them.

‘‘It does mean you will have someone who knows how the levers of power are pushed or how to push the levers, and who can describe to you how situations are going to play out based on their years of experience,’’ said Jim Manley, a former aide to Senator Harry Reid, the majority leader. Manley now works at a Washington lobbying and communications firm, QGA Public Affairs.

In recent interviews, four former aides to Baucus said their ties to him heightened their appeal to potential clients. The link also helped justify their salaries, in some cases $500,000 or higher, more than double or triple their Capitol Hill paychecks.

Former Senate aides who become lobbyists must wait a year before they can contact Baucus or his staff on behalf of a client, according to Senate ethics rules. Staying active in their circle, one former aide said, also requires that they help Baucus’s political career, through fund-raising and other assistance.

No other lawmaker has so many former staffers working as tax lobbyists.

At a gathering last month near the Capitol, Paul Wilkins, Baucus’s chief of staff, talked about the millions of dollars Baucus will need to raise for his reelection campaign next year.

‘‘It allows us to scare off opponents,’’ Wilkins told the group. ‘‘It is the basis of everything that we do. So thank you for your support and everything you have done for Senator Baucus.’’